UW COLLEGES
DEPARTMENT OF MATHEMATICS
10/7/2002
COURSE GUIDELINES
Course Title: Topics in
Geometry
Course No: MAT 081 No. of Credits 3
Course No: MAT 085 No. of Credits 3
Course No: MAT 087 No. of Credits 3
Contact hrs/wk: Lecture 3 Lecture/Discussion Lab
Course Prerequisites: None
Catalog description:
Designed for students who have not had high school geometry. Includes methods of proof, properties of simple plane figures, congruence, and similarity. This course is offered through a contractual arrangement with the local WTCS institution as Mat 085. This course is offered by the campus TRIO/minority/disadvantaged program as Mat 087.
Course content (list of topics normally covered).
Topics marked optional (*) may be covered at the discretion of the course instructor.
The Nature of Deductive Reasoning
Direct Proof
Postulates
Preparing for a Proof
* Indirect Proof
Points, Lines and Planes
The Ruler Postulate
Line Segments
Polygons
Perimeter and area of polygons
Rays and Angles
The Protractor Postulate
Complementary, Supplementary and Vertical Angles
Parallel and Perpendicular Lines
* Elementary Constructions
Congruent Triangles
Congruent Polygons
Isosceles Triangle Theorem
* Proving Triangles Congruent
* Proving Corresponding Parts Equal
* Triangle Constructions
Parallel Postulate
The Parallel Postulate
Consequences of the Parallel Postulate
Quadrilaterals
Parallelograms
Rectangles, Rhombi, Squares and Trapezoids
Area
Polygonal Regions
Squares, Rectangles and Triangles
Parallelograms and Trapezoids
The Right Triangle
Proportions in a Right Triangle
Isosceles and 30°-60° Right Triangles
The Pythagorean Theorem
Circles
Circles, Radii
Circumference and Area of Circles
*Chords and Tangents
*Central Angles and Arcs
*Inscribed and Secant Angles
*Tangent, Chord and Secant Segments
*Circle Constructions
* Sectors and Arcs
Solid Geometry
Lines and Planes in Space
Volumes of Solid Figures
* Inequalities
Exterior Angle Theorem
Triangle Side and Angle Inequalities
Similarity
Ratio and Proportion
Similar Polygons
Similar Triangle Theorem
Perimeters and Areas of Similar Polygons
* Regular Polygons
* Coordinate Geometry
Two-dimensional Coordinate Systems
Distance Formula
Parallel and Perpendicular Lines
Midpoint Formula
Coordinate Proofs
Content-based department proficiencies:
The successful student will:
w recognize connections between geometry and real world objects.
w understand the principles of inductive and deductive reasoning.
w understand common geometric terminology and recognize geometric shapes.
w be able to estimate, measure, and deduce measures of length, angles, area, and volume.
w understand concepts relating to triangles and quadrilaterals.
w know the Pythagorean Theorem and how to use it to determine lengths of sides in a right triangle.
w be able to use formulas appropriately for finding perimeter, area, surface area and volume.
Colleges-wide
proficiencies assigned to course:
w Analyze, synthesize, evaluate and interpret information and ideas.
w Construct and support hypotheses and arguments.
w Solve quantitative and mathematical problems.
w Interpret graphs, tables, and diagrams.
w Integrate knowledge and experience to arrive at creative solutions.
w Recognize fallacies and inconsistencies.
w Write clearly, precisely, and in a well organized manner.
w Develop a large and varied vocabulary.
w Respond orally to questions and challenges.
Representative textbooks used for the courses:
College Geometry, Musser/Trimpe (Prentice Hall)
Elementary Geometry for College Students, 2nd ed., Alexander/Koeberlein (Houghton-Mifflin)
Geometry, Hirsch/Schoen (Scott, Foresman
& Co.)
Geometry, 2nd ed., Jacobs (W.H. Freeman)
Informal Geometry, Smith (Addison-Wesley)